Empirical Cumulative Distribution Function

Compute an empirical cumulative distribution function, with several methods for plotting, printing and computing with such an ecdf object.

hplot, dplot

## S3 method for class 'ecdf': plot(x, \dots, ylab="Fn(x)", verticals = FALSE, col.01line = "gray70", pch = 19)

## S3 method for class 'ecdf': print(x, digits= getOption("digits") - 2, ...)

## S3 method for class 'ecdf': summary(object, \dots) ## S3 method for class 'ecdf': quantile(x, \dots)

x, object
numeric vector of the observations for ecdf; for the methods, an object inheriting from class "ecdf".
arguments to be passed to subsequent methods, e.g., plot.stepfun for the plot method.
label for the y-axis.
see plot.stepfun.
numeric or character specifying the color of the horizontal lines at y = 0 and 1, see colors.
plotting character.
number of significant digits to use, see print.

The e.c.d.f. (empirical cumulative distribution function) $F_n$ is a step function with jumps $i/n$ at observation values, where $i$ is the number of tied observations at that value. Missing values are ignored.

For observations x$= ($$x_1,x_2$, ...$x_n)$, $F_n$ is the fraction of observations less or equal to $t$, i.e., $$F_n(t) = \#{x_i\le t}\ / n = \frac1 n\sum_{i=1}^n \mathbf{1}_{[x_i \le t]}.$$

The function plot.ecdf which implements the plot method for ecdf objects, is implemented via a call to plot.stepfun; see its documentation.


  • For ecdf, a function of class "ecdf", inheriting from the "stepfun" class, and hence inheriting a knots() method.

    For the summary method, a summary of the knots of object with a "header" attribute.

    The quantile(obj, ...) method computes the same quantiles as quantile(x, ...) would where x is the original sample.


The objects of class "ecdf" are not intended to be used for permanent storage and may change structure between versions of R(and did at R3.0.0). They can usually be re-created by eval(attr(old_obj, "call"), environment(old_obj)) since the data used is stored as part of the object's environment.

See Also

stepfun, the more general class of step functions, approxfun and splinefun.

  • ecdf
  • plot.ecdf
  • print.ecdf
  • summary.ecdf
  • quantile.ecdf
library(stats) ##-- Simple didactical ecdf example : x <- rnorm(12) Fn <- ecdf(x) Fn # a *function* Fn(x) # returns the percentiles for x tt <- seq(-2, 2, by = 0.1) 12 * Fn(tt) # Fn is a 'simple' function {with values k/12} summary(Fn) ##--> see below for graphics knots(Fn) # the unique data values {12 of them if there were no ties} y <- round(rnorm(12), 1); y[3] <- y[1] Fn12 <- ecdf(y) Fn12 knots(Fn12) # unique values (always less than 12!) summary(Fn12) summary.stepfun(Fn12) ## Advanced: What's inside the function closure? ls(environment(Fn12)) ##[1] "f" "method" "n" "x" "y" "yleft" "yright" utils::ls.str(environment(Fn12)) stopifnot(all.equal(quantile(Fn12), quantile(y))) ###----------------- Plotting -------------------------- require(graphics) op <- par(mfrow = c(3, 1), mgp = c(1.5, 0.8, 0), mar = .1+c(3,3,2,1)) F10 <- ecdf(rnorm(10)) summary(F10) plot(F10) plot(F10, verticals = TRUE, do.points = FALSE) plot(Fn12 , lwd = 2) ; mtext("lwd = 2", adj = 1) xx <- unique(sort(c(seq(-3, 2, length = 201), knots(Fn12)))) lines(xx, Fn12(xx), col = "blue") abline(v = knots(Fn12), lty = 2, col = "gray70") plot(xx, Fn12(xx), type = "o", cex = .1) #- plot.default {ugly} plot(Fn12, col.hor = "red", add = TRUE) #- plot method abline(v = knots(Fn12), lty = 2, col = "gray70") ## luxury plot plot(Fn12, verticals = TRUE, col.points = "blue", col.hor = "red", col.vert = "bisque") ##-- this works too (automatic call to ecdf(.)): plot.ecdf(rnorm(24)) title("via simple plot.ecdf(x)", adj = 1) par(op)
Documentation reproduced from package stats, version 3.3, License: Part of R 3.3

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